There is actually evidence supporting the idea that on average pedophiles have below average intelligence. One study showed that the lower a persons age of attraction is below societal norms, the lower below average their IQ is likely to be (with pedophile average IQ being significantly below average, hebephile average IQ being slightly below average, and teliophile IQ being average). There is also a positive correlation between childhood head injury and pedophilia. Of course there are always exceptions though, some of the online pedophile groups clearly consist of members with superior intelligence.